{
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  "cpu_threads": 1,
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  "elapsed_seconds": 331.77217996400003,
  "script_sha256": "913dfda878caa227e47a8d147ee664bbc8e352a42905f8d1279222529f99fe0c",
  "rendering_coordinates": "imshow pixel edges from stored physical sample centers; axes cropped to requested full/design extent",
  "grid_shape": [
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  "f_initial": 2.9157725347233225,
  "f_updated": 38.414729650998424,
  "gradient_gate": {
    "passed": true,
    "max_relative_error": 1.8392736457117047e-05,
    "checks": [
      {
        "step_l2": 0.01,
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  "update_method": "one projected gradient-ascent step with backtracking",
  "step": 0.15,
  "export_pixels": 720,
  "native_field_sampling": "60 pixels/um; 1um design region; raster export uses nearest samples without smoothing",
  "raw_arrays": "fields.npz (packaged with reproducibility source, outside static-site assets)",
  "scene_rendering": {
    "source": "saved complex128 full-cell Ez DFT, fields.npz",
    "source_sha256": "fad41cb79f2812e8172acabc5fdd074557c501b31614a77c7f5a5af53ace5aed",
    "quantity": "Re(Ez * exp(-i phase)); saved complex DFT phasor",
    "colormap": "bwr_r",
    "display_style": "approved wavefront + gray fixed geometry and continuous density; display-only change",
    "geometry_background": "fixed guides and continuous design density, not sampled epsilon; no thresholding",
    "opacity": "sqrt(abs(Re(Ez))/symmetric_limit); visual compositing only",
    "sign": "negative red; zero white; positive blue",
    "full_extent_um": [
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      3.0,
      -2.5,
      2.5
    ],
    "design_extent_um": [
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      -0.5,
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    "scene_pixels": [
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    "capture_pixels": [
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    "native_design_pixels": [
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    "native_spacing_um": 0.016666666666666666,
    "orientation": "field[col,Ny-1-row]; top is +y; bwr_r overlay on density background",
    "capture_rendering": "exact full-scene design crop, nearest enlargement, black boundary and centered port markers",
    "phase_frame_count": 32,
    "phase_columns": 8,
    "phase_rows": 4,
    "phase_convention": "phase_k = 2*pi*k/32; Re(F*exp(-i*phase_k)); phase0 is the original real phasor",
    "normalization": "fixed symmetric +/-max(abs(complex full Ez)) per calculation, shared by every phase, scene, capture",
    "notTransient": true,
    "provenance": "DFT phase cycle / steady state; no wavefront arrival, source turn-on, or propagation delay",
    "scenes": {
      "forward": {
        "scene": "forward-scene.png",
        "symmetric_limit": 20.31869826702306,
        "vmin": -20.31869826702306,
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        "sprite": "forward-phases.png",
        "sprite_pixels": [
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        "quarter_cycle_max_absolute_errors": {
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          "8": 8.881784197001252e-16,
          "16": 1.7763568394002505e-15,
          "24": 3.552713678800501e-15
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        "loop_closure_max_absolute_error": 4.440892098500626e-15,
        "saved_all_frames_match": true,
        "animated_content": true,
        "capture": "forward-capture.png",
        "capture_limit": 20.31869826702306,
        "scene_crop_box_pixels": [
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        "capture_matches_scene_interior": true,
        "frame0_capture_match": true,
        "frame0_scene_match": true
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      "adjoint": {
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        "sprite": "adjoint-phases.png",
        "sprite_pixels": [
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        "quarter_cycle_max_absolute_errors": {
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          "8": 2.168404344971009e-19,
          "16": 4.336808689942018e-19,
          "24": 4.336808689942018e-19
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        "loop_closure_max_absolute_error": 6.505213034913027e-19,
        "saved_all_frames_match": true,
        "animated_content": true,
        "capture": "adjoint-capture.png",
        "capture_limit": 0.0030279939741658535,
        "scene_crop_box_pixels": [
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        "capture_matches_scene_interior": true,
        "frame0_capture_match": true,
        "frame0_scene_match": true
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      "updated-forward": {
        "scene": "updated-forward-scene.png",
        "symmetric_limit": 18.579813822588232,
        "vmin": -18.579813822588232,
        "vmax": 18.579813822588232
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    },
    "input_phase_direction_check": {
      "sample_x_range_um": [
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      "sample_y_um": -0.008333333333333304,
      "phase_slope_rad_per_um": 13.125825966783962,
      "convention": "positive spatial phase slope with exp(-i phase) advances constant phase toward +x",
      "direction": "source to design (+x)",
      "passed": true,
      "interpretation": "total steady-state field may also contain reflected waves; this is not transient arrival"
    }
  }
}